(a) Answer angle of elevation = 39.4 ∘ Explanation Given information: Railways: The steepest railway in the world is the Katoomba Scenic Railway in Australia. The passenger car is pulled up the mountain by twin steel cables. It travels along the track 1020 feet to obtain a change in altitude of 647 feet. Calculation: This is the sketch of the triangle. From our angle of elevation we have the opposite and hypotenuse so use sin − 1 sin − 1 647 1020 = angle of elevation angle of elevation = 39.4 ∘ (b) To determine How far does the car travel in a horizontal direction? Answer 788 feet Explanation Given information: Railways: The steepest railway in the world is the Katoomba Scenic Railway in Australia. The passenger car is pulled up the mountain by twin steel cables. It travels along the track 1020 feet to obtain a change in altitude of 647 feet. Calculation: The horizontal distance the train travels is the “ x ” in the sketch. We know now the angle is 39.4 ∘ and we are looking for the adjacent side, so we can do cosine or tangent. Cosine is my choice. cos 39.4 ∘ = x 1020 x = 1020 × cos 39.4 ∘ x = 788 feet

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

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Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

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Question

Chapter 5.5, Problem 44E

(a)

To determine

To find: The angle of elevation of the railway.

(a)

Expert Solution

Answer to Problem 44E

angle of elevation=39.4∘

Explanation of Solution

Given information: Railways: The steepest railway in the world is the Katoomba Scenic Railway in Australia. The passenger car is pulled up the mountain by twin steel cables. It travels along the track 1020 feet to obtain a change in altitude of 647 feet.

Calculation:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.5, Problem 44E

This is the sketch of the triangle. From our angle of elevation we have the opposite and hypotenuse so use sin−1

sin−16471020=angle of elevationangle of elevation=39.4∘

(b)

To determine

How far does the car travel in a horizontal direction?

(b)

Expert Solution

Answer to Problem 44E

788 feet

Explanation of Solution

Calculation:

The horizontal distance the train travels is the “ x ” in the sketch. We know now the angle is 39.4∘ and we are looking for the adjacent side, so we can do cosine or tangent. Cosine is my choice.

cos39.4∘=x1020x=1020×cos39.4∘x=788 feet

Chapter 5.5, Problem 43E

Chapter 5.5, Problem 45E

Chapter 5 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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